Waveform inversion of a stacked section using an exploding reflector concept

Abstract

Waveform inversion is one of the valuable methods for seismic interpretation. Most of the waveform inversion algorithms employ common shot gathers. Since we obtain stacked data in general seismic data processing, there are needs to develop a waveform inversion algorithm that can be applied to stacked data. We design a waveform inversion algorithm using exploding reflectors, which is applied to stacked data. Our algorithm is constructed under the assumptions that there exist many exploding reflectors and waves excited at the reflectors propagate with half a velocity as in poststack migration. In our inversion algorithm, we choose the steepest-descent method, and compute the steepest-descent direction by introducing a backpropagation technique and virtual source concept, which are popularly used in frequencydomain waveform inversion these days. The virtual source is regarded as a source for partial derivative wavefield with respect to subsurface velocity, therefore we compute the virtual source by taking the derivative of the modeling operator with respect to subsurface velocity. In the conventional waveform inversion using the steepest-descent method, since original sources, used in forward modeling, are independent of subsurface velocity, the virtual source does not include any original source-related term. In our waveform inversion, however, we use subsurface exploding reflectors for original sources in forward modeling. Since the exploding reflectors are expressed by subsurface velocity contrasts, the virtual source has terms generated by taking the derivative of original sources with respect to subsurface velocity. Numerical structure of our waveform inversion is really similar to that of the conventional one except for different virtual source and different velocity (i.e., half a velocity). We apply our algorithm to a field data set, which was gathered in the Korean continental shelf. In our inversion results, we could observe an anticlinal structure clearly, which is already known to be gas reservoir.